Is it mostly the case to train with available models
Yes, it is recommended to start with pre-trained model if you don't have high-end hardware. You can use a pre-trained model for fine-tuning (their trained weight as your initial weight) or use it as feature extractor (you remove few last layers, and then train it).
Why we need a pre-trained network?

Because training a good deep model takes a lot of time and needs a lot of hardware. Some good models, like DenseNet, ResNet, even VGG16 need days of training. You can read from VGG original paper:

On a system equipped with four NVIDIA Titan Black GPUs, training a single net took 2–3 weeks depending on the architecture.


Sometimes our case is similar to the dataset of pre-trained models out there. For example, if we need to classify some images of flower type, even our case has different class, we can use some first Convolutional layers of pre-trained model and use it as a feature extractor.


You can read more about transfer learning from this paper or this page.